Summary: Eur. J. Phys. 20 (1999) 153­159. Printed in the UK PII: S0143-0807(99)99917-8
Is the number of photons a classical
invariant?
J E Avron, E Berg, D Goldsmith and A Gordon
Department of Physics, Technion, 32000 Haifa, Israel
Received 3 December 1998
Abstract. We describe an apparent puzzle in classical electrodynamics and its resolution. It is
concerned with the Lorentz invariance of the classical analogue of the number of photons.
1. Introduction
Photons are quantum objects and a priori have no business in classical electrodynamics. So,
what can one possibly mean by the question `Is the number of photons a classical invariant?'
Consider a box filled with monochromatic radiation of frequency . If U denotes the total
electromagnetic energy in the box, then, the right-hand side of
¯hN =
U

(1)
is a purely classical quantity. The left-hand side gives the interpretation and quantization of
this quantity, namely, that it counts the number of photons, N, in units of ¯h. What then is the
classical significance of U/?